# How do I convert lens mm to optical zoom times?

What is the rule to convert the 'mm' notation to the 'optical zoom' notation? I searched a bit and found this one:

``````optical zoom = maximum focal length / minimum focal length
``````

For example a 18-55mm lens would have a 3x optical zoom, and a 18-200mm lens would have a 11x optical zoom. Is that right?

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Related: What does 'how much zoom' mean? – mattdm Jul 3 '11 at 22:44
The "mm notation" is the focal length. Note that when computing the zoom ratio (e.g. 3x, 5x) the units cancel so you can quote the focal length in inches, meters, AU and it won't influence the calculation. – Matt Grum Jul 3 '11 at 22:56
You are right. 55/18 = 3, 200/18 = 11. That's it :-) – Darksair Nov 26 '11 at 16:20
@MattGrum - I hope I will live to see an AU lens in my time... ;-) – ysap Nov 30 '11 at 14:30
May I ask why you want to know this? Its not a very meaningful metric. – Pat Farrell Sep 8 '12 at 22:04
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The "times zoom" notation is simply the big number divided by the small one, so the examples you give are correct. "3x zoom" simply means the longest focal length is three times the shortest.

This number really isn't very useful, though. On point and shoot cameras, it became popular because the starting focal length was generally about the same across all models — a wide-normal field of view. That makes the times-zoom a reasonable indicator of how far one can zoom in to get a closer view of a distant subject. But with interchangeable lenses, that's less likely to be true, so it's not really so useful on its own. An 18-55mm and a 70-200mm are both about "3x zoom", but a very different range.

On the other hand, the zoom ratio does give you an idea of how much focal length flexibility the lens has, and usually higher numbers are a clue that there will be more compromise on image quality (and/or price, size, and weight).

This is a field with a lot of jargon and a lot of numbers to learn. That can be intimidating to would-be photographers who want to concentrate on images, not "tech stuff". A simple number, without any metric-system units, is far less intimidating than needing to learn all about focal length and angle of view, so I don't think the marketers are all wrong to focus on this number for basic cameras.

For interchangeable lens cameras, like digital SLRs or mirrorless compact system cameras, in some ways the complexity of using focal lengths is a selling point. Intermediate and advanced users may prefer to be given the straightforward facts instead of having to decode more-removed numbers like times-zoom. In some ways, giving the angle of view instead of focal length might be preferable, but that hasn't really caught on — probably because it's really not very hard to get a sense for what different focal lengths mean for field of view on your own camera, once you get over the initial learning bump.

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+1 Thx for editing and answering (comprehensively) my question ;) – DiAlex Jul 3 '11 at 23:09
yay for my 0x zoom 35mm f/2.0 Nikkor :) – jwenting Jul 5 '11 at 6:27
@jwenting Technically that would be a 1x zoom. – Evan Krall Nov 27 '11 at 5:38
@EvanKrall depends on your definition of the term. It doesn't zoom at all, 1x would to me indicate it has a range of y to 2 time y mm focal length (1 times more than the base) :) – jwenting Nov 28 '11 at 6:54
@jwenting That'd make the 18-55 a 2x zoom and the 18-200 a 10x zoom. It doesn't fit the convention. – Evan Krall Nov 29 '11 at 7:40

That's exactly what it means. The "zoom power" of a lens has no meaning except as the relationship between the longest and shortest focal length of the lens. For instance, even on a "bridge" or "ultrazoom" camera, one camera being marketed as a 30X zoom and another as a 28X zoom doesn't tell you whether the longest field of view is longer or the widest is wider, just that the lens has a greater range between the two.

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Yes you are correct both are 3x lenses. I think you you may be confused with the terminology from the compact camera world. When you are talking about compact most cameras have nearly identical widest focal length. This may be the cause of your confusion. For example this page from dpreview from lists canon compact and their zoom ratios. You can see that Canon PowerShot ELPH 320 HS (IXUS 240 HS) and Canon PowerShot A2300 are both listed as 5x cameras but the focal length of the earlier model is 24 – 120 mm whereas the later is 28 – 140 mm.

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There is also another thing to consider. As you zoom in with linearly in millimetres, the actual field of view change is not linear. Zooming 2mm in when at 17mm will result in a much larger change in the field of view than zooming 2mm further at 200mm.

It will depend on how you define the "zoom factor". Is it field of view or focal length?

EDIT

Here is the actual field of view graph for 1mm increments from 15mm to 200mm on a 35mm SLR. This was generated at http://www.howardedin.com/articles/fov.html and the diagonal was made simply with the hypotenuse algorithm `h²=x²+y²`. The graph itself shows in 5mm increments.

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Just focal length, I'm only considering the magnification of the image. – DiAlex Jul 3 '11 at 23:03
Actually, I think it is linear, isn't it? In the first case, it'll be a 2/17=11.8% change, and in the second, it's 2/200=1%. That's because zooming is mathematically like cropping, so each doubling of focal length is halving dimensional field of view in a very straightforward way. – mattdm Jul 3 '11 at 23:07
slaps forehead Why didn't I even think of that... – Nick Bedford Jul 3 '11 at 23:28
Nick Bedford, @mattdm - I'd stress that the actoal FoV change is indeed nonlinear. For relatively long focal lengths, the angles are small and the change is approximately linear. However, as you get to the wider side, the angles become large and the mapping from focal length to angle of view is nonlinear. That said, I never saw a definition of zoom range w.r.t change in FoV. – ysap Jul 4 '11 at 16:28
Updated with a graph showing the field of view. – Nick Bedford Jul 4 '11 at 22:27